Found this old childhood photo of myself from 2016 doing the TENET gesture, I was MINDBLOWN as TENET is now one of my favorite movies OAT.

Sator "always had instincts about the future" and his mobile device must be his good assistant in this regard. At least he holds it in his hand while saying that phrase to Kat on the boat and looks at it two more times in Tallinn when he is inverted: just after running from the turnstile (more notably) and after grabbing Kat from a chair (at a glance). Since every scene in Tenet is meticulously crafted, this device must be something very important to Sator. He managed to move the painting from the Oslo freeport to a safe place before the TP and Neil compromised the building. And while saying this to Kat, he holds the device in his hand. Why is it so important in launching a TPM in Tallinn? Volkov revealed all the information to him from the highway, but was Sator looking for some hints on the matter from the future?